On Generalized Stieltjes Functions

Stamatis Koumandos; Henrik L. Pedersen

doi:10.1007/s00365-018-9440-8

On Generalized Stieltjes Functions

Stamatis Koumandos, Henrik L. Pedersen^*

^*Corresponding author for this work

Department of Mathematical Sciences

3 Citations (Scopus)

30 Downloads (Pure)

Abstract

It is shown that a function f is a generalized Stieltjes function of order λ> 0 if and only if x1-λ(xλ-1+kf(x))(k) is completely monotonic for all k≥ 0 , thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions f for which x1-λ(xλ-1+kf(x))(k) is completely monotonic for all k≤ n is obtained in terms of properties of the representing measure of f.

Original language	English
Journal	Constructive Approximation
Volume	50
Issue number	1
Pages (from-to)	129-144
ISSN	0176-4276
DOIs	https://doi.org/10.1007/s00365-018-9440-8
Publication status	Published - 15 Aug 2019

Keywords

Completely monotonic function
Generalized Stieltjes function
Laplace transform

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AU - Pedersen, Henrik L.

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N2 - It is shown that a function f is a generalized Stieltjes function of order λ> 0 if and only if x1-λ(xλ-1+kf(x))(k) is completely monotonic for all k≥ 0 , thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions f for which x1-λ(xλ-1+kf(x))(k) is completely monotonic for all k≤ n is obtained in terms of properties of the representing measure of f.

AB - It is shown that a function f is a generalized Stieltjes function of order λ> 0 if and only if x1-λ(xλ-1+kf(x))(k) is completely monotonic for all k≥ 0 , thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions f for which x1-λ(xλ-1+kf(x))(k) is completely monotonic for all k≤ n is obtained in terms of properties of the representing measure of f.

KW - Completely monotonic function

KW - Generalized Stieltjes function

KW - Laplace transform

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DO - 10.1007/s00365-018-9440-8

M3 - Journal article

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EP - 144

JO - Constructive Approximation

JF - Constructive Approximation

IS - 1

ER -

On Generalized Stieltjes Functions

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